There are two stages to an eviction. The first is the termination notice which concludes the current leases and contains the date by which the tenant has to leave.
The second is the “termination order” aka eviction notice, which can only be issued by the tribunal (NCAT), which a landlord would seek if their tenant failed to leave the premises despite having been given due notice.
From what I hear, your chances of getting a hearing at NCAT in the next few months are between zero and zilch.
However, my understanding is that if the tenant refused to leave, they would still be bound by the terms of the existing lease until such times as they did leave or signed another lease. It is therefore in your tenant’s interest to come to some kind of mutually acceptable arrangement with you.
A very good source of information is the Tenants Union website where factsheets like this one will help to ensure you are operating within the law, and not unfairly treating the tenant, whatever happens.